The new head of a Brooklyn high school that was engulfed in a grade-fixing scandal last year vowed Tuesday to ban the shady shortcuts used to boost the graduation rate.

Dewey HS Principal Connie Hamilton told teachers she wants to wipe the slate clean and restore the Gravesend school’s reputation, which was shattered by her predecessor, Kathleen Elvin.

Schools Chancellor Carmen Fariña removed Elvin in June after city investigators confirmed stories in The Post that the then-principal masterminded sham “credit recovery” courses — dubbed “Easy Pass” by students — to boost the graduation rate.

In conversations with teachers during their first day back at school on Tuesday, Hamilton said there will no pass-rate or graduation-rate “quotas” or phony credit-recovery courses to make the school look better.

The results of achievement must be honest and real — even if it means a drop in the graduation rate in the short term, she and her team told teachers.

Instructors at the 1,900-student school, who were terrified of Elvin, welcomed the new approach.

“There’s a very hopeful mood than we can turn a corner and start anew. Principal Hamilton wants to restore the integrity of the school. She understands what was done,” said veteran social-studies teacher Wade Goria.

Other teachers said it would take time to heal the wounds and rebuild trust at the school — especially since many of the administrators who pressured them to pass kids are still there.

In some of the credit-recovery courses, students weren’t given any instruction but received passing grades anyway, according to an investigative report.

Michael Klimetz, a physics teacher at Dewey for 21 years, said Hamilton is a “breath of fresh air.”

But he added, “I am discouraged to see the same assistant principals here . . . Some of the same assistant principals that were part of the whole grade-manipulation scheme are still here.”

He said he broached the issue with Hamilton and was told she is retraining the assistant principals and has brought in new supervisors to implement her restructuring.

“It’s going to take a lot more than a promise to restore the school’s integrity. She is eager to bring things back to as healthy as they can be. Time will tell,” Klimetz said.

Math teacher Konstantin Petrov said he is hopeful that teaching will take precedence over pass rates.

“I hope there will be more responsibility for learning. You know that ‘Easy Pass’ mentality — none of the teachers liked it. I hope the students will have more responsibility and will really be graded for their knowledge. I hope there will be less pressure to pass students,” he said.

Another staffer said, “There’s absolute relief in the building. Everyone seems to understand we won’t pass students who don’t deserve to be passed, even if it means the graduate rate takes a hit.

“We’re ready to start working with a supportive administration.”

Following Elvin’s ouster, the Department of Education agreed to reverse the negative job ratings of at least four Dewey teachers. Instructors claimed they received ineffective ratings because they wouldn’t rig student grades.